Marginal effects of Multinomial Logit

[Xiaocan Yuan]

Hi everyone!

I am new in the forum. Hope any of you with expertise can share advice with me.
I have come across a question about the average marginal effects as I kept gaining the same average marginal effects results after changing the based group when running a mlogit regression.

My commands:
mlogit y x1 x2, based(1)
margins, dydx(*)

mlogit y x1 x2, based(2)
margins, dydx(*)

I was hoping to find out why that's the case or is there anything wrong with my commands? Marginal effects stand for the probability relative to the based group, and I suppose it should be different when the based group is changed?

Many thanks in advance.
Xiaocan

[Clyde Schechter]

First, there is no -based()- option in -mlogit- and the commands you show will produce only error messages. Are you perhaps referring to the -baseoutcome()- option?

Next,

Marginal effects stand for the probability relative to the based group, and I suppose it should be different when the based group is changed?

is simply incorrect. The regression coefficients give you log risk ratios relative to the base outcome in the -mlogit- output. But -margins- is different. The output of -margins, dydx()- gives you the difference in probability of each of the outcome level associated with a unit change in each predictor variable. This is given for each of the outcome levels and is completely independent of the baseoutcome specified.

[Xiaocan Yuan]

Thank you so much for your reply Prof. Schechter.
And apologise for the typo. Yes, I was referring to the baseoutcome(#) option.

Thanks for the clear explanation and I am clear now.

[Xiaocan Yuan]

Hi Prof. Schechter, I have got a bit confusing again when interpreting the meaning of marginal effects. I got your point that margins are independent of the specified baseoutcome. However, when we interpret its meaning, shall I say that one unit increase of x is associated with an additive increase of x percentage compared with the base rate? (please see from the link: https://www.statalist.org/forums/for...-margins-stata)

If the base rate should be specified here (or to say, baseoutcome), how I can avoid confusion when interpreting if marginal effects are the same under a different baseoutcome(#)?

Thanks again!

[Clyde Schechter]

However, when we interpret its meaning, shall I say that one unit increase of x is associated with an additive increase of x percentage compared with the base rate?

No, you should not say that, precisely because it invites the misunderstanding that motivated your original post. The term "base" is ambiguous in this context and should be avoided.

For each of the different outcome levels, the marginal effect of x on that outcome level is that a unit difference in x is associated with a difference in [insert output for this outcome level from -margins, dydx(x)- here] the probability of this outcome.

I cannot emphasize too strongly that the outputs of -margins, dydx()- here are not relative to the baselevel of the outcome variable. They are just associated with unit changes in the predictor variable(s). This is the opposite of the outputs of -mlogit- itself, which are relative to the baselevel of the outcome variable.

[Xiaocan Yuan]

Thanks again for your clear explanation Prof. Schechter.
That's of great help and will keep your advice in mind.

[Dariusz Andrejuk]

Hi Prof. Schechter,
To sum up, am I correct when saying according to such results:
(example)
dy/dx
variable: having child
for outcome 1: dy/dx 0.02 significant
for outcome 2: dy/dx -0.12 significant
for outcome 3: dy/dx 0.10 significant

The probability of outcome 1 is 2% higher when there is a child in a household (in comparison to all other outcomes?).
Having child decreases the probability of outcome 2 by 12% (in comparison to all other outcomes?). Or maybe I should say "percentage points"?

If I am right, I have another question:
Is there a possibility to get a result showing the change in probability of one outcome in comparison to other one outcome. I want to know for example:

The probability of outcome 1 is ..... higher/lower when there is a child in a household IN COMPARISON WITH OUTCOME 2 and ..... higher/lower IN COMPARISON WITH OUTCOME 3.

I would be very grateful for your help


Thank you in advance

[Clyde Schechter]

You have not provided the necessary information to answer your questions. Those results cannot be interpreted without seeing the regression command and the margins commands themselves. Show those along with the complete -margins- output.

[Clara Matthis]

I am running a multinominal logit regression with five dependent variable categories: "1", "2", "3", "4" and "5". I computed marginal effects in Stata (margins dy/dx in Stata), which show the difference in probability of each of the dependent variable categories associated with a one unit change in each of the independent variables. Only the marginal effect for "3" is significant and negative for one of the independent variables. If the mean of the dependent variable is "4", can I then conclude that the independent variable has a positive effect on the dependent variable?

[Clyde Schechter]

What does "has a positive effect on the dependent variable" mean?

Also, if you accept that the 1-5 rating scale satisfies the conditions necessary for calculation of its mean value to be meaningful, why are you analyzing it with -mlogit- which treats it a purely arbitrary category variable?

[Clara Matthis]

Yes, the dependent variable is ordered, however the assumptions for ordered logit regression were not fulfilled. The values 1-5 correspond to survey answers ranging from no agreement (1) to full agreement (5). The mean value is (4). I ran a multinominal logit regression and then calculated marginal effects, which give me the change in probability of each of the dependent variable outcomes associated with a one unit change in the independent variables. I.e. if the marginal effects of the independent variable xi are positive and significant for outcomes 4 and 5, I can conclude a positive effect of xi on the dependent variable, as xi leads to a higher level of agreement, if the probability for the two high agreement categories (4 and 5) increases. If the marginal effect of xi is negative and only significant for outcome 3 and the mean of the dependent variable is 4, can this be interpreted as a positive effect, as it shows that outcome 3 is less likely (effects on 1 and 2 are negative and 4 and 5 positive, but insignificant)?

[Clyde Schechter]

Yes, the dependent variable is ordered, however the assumptions for ordered logit regression were not fulfilled.

Not my point. The fact that you are taking a mean suggests that you believe this variable has interval-level variable, which is beyond merely being ordered. So why aren't you just treating it as such and using simple linear regression?

If the marginal effect of xi is negative and only significant for outcome 3 and the mean of the dependent variable is 4, can this be interpreted as a positive effect, as it shows that outcome 3 is less likely (effects on 1 and 2 are negative and 4 and 5 positive, but insignificant)?

I wouldn't buy that argument. I might be persuaded if I saw the actual marginal effects themselves. You could even calculate the marginal effect on the mean response from the prevalence of each response category in the absence of an xi effect. But the statistical significance of those marginal effects is really uninformative about this.